Let \(U = [0,1] \times \lbrace 0\rbrace  \times [0,1]\)  and let \(\kappa \colon [0,1]^2 \rightarrow \mathbb {R}\)  be a nonnegative smooth function with \(\operatorname{supp}\kappa \subset (0,1)^2\) . We require that \(\Vert \kappa \Vert _\infty \le 1\) , \(\kappa (s,t) > 0\)  for \(s,t\in [\frac{1}{5}, \frac{4}{5}]\) , and that the partial derivatives of \(\kappa \)  of order at most 2 are all in the interval \([-1,1]\) . (The assumption on partial derivatives is used in [1]} to bound certain derivatives when \(\rho \ge 8\) ; it can be dropped at the cost of changing some constants.)
